direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C5×C11⋊C8, C55⋊4C8, C11⋊3C40, C22.3C20, C44.6C10, C220.4C2, C110.4C4, C20.4D11, C10.3Dic11, C4.2(C5×D11), C2.(C5×Dic11), SmallGroup(440,4)
Series: Derived ►Chief ►Lower central ►Upper central
| C11 — C5×C11⋊C8 |
Generators and relations for C5×C11⋊C8
G = < a,b,c | a5=b11=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C5×C11⋊C8
►Regular action on 440 points
Generators in S440
(1 177 133 89 45)(2 178 134 90 46)(3 179 135 91 47)(4 180 136 92 48)(5 181 137 93 49)(6 182 138 94 50)(7 183 139 95 51)(8 184 140 96 52)(9 185 141 97 53)(10 186 142 98 54)(11 187 143 99 55)(12 188 144 100 56)(13 189 145 101 57)(14 190 146 102 58)(15 191 147 103 59)(16 192 148 104 60)(17 193 149 105 61)(18 194 150 106 62)(19 195 151 107 63)(20 196 152 108 64)(21 197 153 109 65)(22 198 154 110 66)(23 199 155 111 67)(24 200 156 112 68)(25 201 157 113 69)(26 202 158 114 70)(27 203 159 115 71)(28 204 160 116 72)(29 205 161 117 73)(30 206 162 118 74)(31 207 163 119 75)(32 208 164 120 76)(33 209 165 121 77)(34 210 166 122 78)(35 211 167 123 79)(36 212 168 124 80)(37 213 169 125 81)(38 214 170 126 82)(39 215 171 127 83)(40 216 172 128 84)(41 217 173 129 85)(42 218 174 130 86)(43 219 175 131 87)(44 220 176 132 88)(221 397 353 309 265)(222 398 354 310 266)(223 399 355 311 267)(224 400 356 312 268)(225 401 357 313 269)(226 402 358 314 270)(227 403 359 315 271)(228 404 360 316 272)(229 405 361 317 273)(230 406 362 318 274)(231 407 363 319 275)(232 408 364 320 276)(233 409 365 321 277)(234 410 366 322 278)(235 411 367 323 279)(236 412 368 324 280)(237 413 369 325 281)(238 414 370 326 282)(239 415 371 327 283)(240 416 372 328 284)(241 417 373 329 285)(242 418 374 330 286)(243 419 375 331 287)(244 420 376 332 288)(245 421 377 333 289)(246 422 378 334 290)(247 423 379 335 291)(248 424 380 336 292)(249 425 381 337 293)(250 426 382 338 294)(251 427 383 339 295)(252 428 384 340 296)(253 429 385 341 297)(254 430 386 342 298)(255 431 387 343 299)(256 432 388 344 300)(257 433 389 345 301)(258 434 390 346 302)(259 435 391 347 303)(260 436 392 348 304)(261 437 393 349 305)(262 438 394 350 306)(263 439 395 351 307)(264 440 396 352 308)
(1 2 3 4 5 6 7 8 9 10 11)(12 13 14 15 16 17 18 19 20 21 22)(23 24 25 26 27 28 29 30 31 32 33)(34 35 36 37 38 39 40 41 42 43 44)(45 46 47 48 49 50 51 52 53 54 55)(56 57 58 59 60 61 62 63 64 65 66)(67 68 69 70 71 72 73 74 75 76 77)(78 79 80 81 82 83 84 85 86 87 88)(89 90 91 92 93 94 95 96 97 98 99)(100 101 102 103 104 105 106 107 108 109 110)(111 112 113 114 115 116 117 118 119 120 121)(122 123 124 125 126 127 128 129 130 131 132)(133 134 135 136 137 138 139 140 141 142 143)(144 145 146 147 148 149 150 151 152 153 154)(155 156 157 158 159 160 161 162 163 164 165)(166 167 168 169 170 171 172 173 174 175 176)(177 178 179 180 181 182 183 184 185 186 187)(188 189 190 191 192 193 194 195 196 197 198)(199 200 201 202 203 204 205 206 207 208 209)(210 211 212 213 214 215 216 217 218 219 220)(221 222 223 224 225 226 227 228 229 230 231)(232 233 234 235 236 237 238 239 240 241 242)(243 244 245 246 247 248 249 250 251 252 253)(254 255 256 257 258 259 260 261 262 263 264)(265 266 267 268 269 270 271 272 273 274 275)(276 277 278 279 280 281 282 283 284 285 286)(287 288 289 290 291 292 293 294 295 296 297)(298 299 300 301 302 303 304 305 306 307 308)(309 310 311 312 313 314 315 316 317 318 319)(320 321 322 323 324 325 326 327 328 329 330)(331 332 333 334 335 336 337 338 339 340 341)(342 343 344 345 346 347 348 349 350 351 352)(353 354 355 356 357 358 359 360 361 362 363)(364 365 366 367 368 369 370 371 372 373 374)(375 376 377 378 379 380 381 382 383 384 385)(386 387 388 389 390 391 392 393 394 395 396)(397 398 399 400 401 402 403 404 405 406 407)(408 409 410 411 412 413 414 415 416 417 418)(419 420 421 422 423 424 425 426 427 428 429)(430 431 432 433 434 435 436 437 438 439 440)
(1 263 34 241 12 252 23 230)(2 262 35 240 13 251 24 229)(3 261 36 239 14 250 25 228)(4 260 37 238 15 249 26 227)(5 259 38 237 16 248 27 226)(6 258 39 236 17 247 28 225)(7 257 40 235 18 246 29 224)(8 256 41 234 19 245 30 223)(9 255 42 233 20 244 31 222)(10 254 43 232 21 243 32 221)(11 264 44 242 22 253 33 231)(45 307 78 285 56 296 67 274)(46 306 79 284 57 295 68 273)(47 305 80 283 58 294 69 272)(48 304 81 282 59 293 70 271)(49 303 82 281 60 292 71 270)(50 302 83 280 61 291 72 269)(51 301 84 279 62 290 73 268)(52 300 85 278 63 289 74 267)(53 299 86 277 64 288 75 266)(54 298 87 276 65 287 76 265)(55 308 88 286 66 297 77 275)(89 351 122 329 100 340 111 318)(90 350 123 328 101 339 112 317)(91 349 124 327 102 338 113 316)(92 348 125 326 103 337 114 315)(93 347 126 325 104 336 115 314)(94 346 127 324 105 335 116 313)(95 345 128 323 106 334 117 312)(96 344 129 322 107 333 118 311)(97 343 130 321 108 332 119 310)(98 342 131 320 109 331 120 309)(99 352 132 330 110 341 121 319)(133 395 166 373 144 384 155 362)(134 394 167 372 145 383 156 361)(135 393 168 371 146 382 157 360)(136 392 169 370 147 381 158 359)(137 391 170 369 148 380 159 358)(138 390 171 368 149 379 160 357)(139 389 172 367 150 378 161 356)(140 388 173 366 151 377 162 355)(141 387 174 365 152 376 163 354)(142 386 175 364 153 375 164 353)(143 396 176 374 154 385 165 363)(177 439 210 417 188 428 199 406)(178 438 211 416 189 427 200 405)(179 437 212 415 190 426 201 404)(180 436 213 414 191 425 202 403)(181 435 214 413 192 424 203 402)(182 434 215 412 193 423 204 401)(183 433 216 411 194 422 205 400)(184 432 217 410 195 421 206 399)(185 431 218 409 196 420 207 398)(186 430 219 408 197 419 208 397)(187 440 220 418 198 429 209 407)
G:=sub<Sym(440)| (1,177,133,89,45)(2,178,134,90,46)(3,179,135,91,47)(4,180,136,92,48)(5,181,137,93,49)(6,182,138,94,50)(7,183,139,95,51)(8,184,140,96,52)(9,185,141,97,53)(10,186,142,98,54)(11,187,143,99,55)(12,188,144,100,56)(13,189,145,101,57)(14,190,146,102,58)(15,191,147,103,59)(16,192,148,104,60)(17,193,149,105,61)(18,194,150,106,62)(19,195,151,107,63)(20,196,152,108,64)(21,197,153,109,65)(22,198,154,110,66)(23,199,155,111,67)(24,200,156,112,68)(25,201,157,113,69)(26,202,158,114,70)(27,203,159,115,71)(28,204,160,116,72)(29,205,161,117,73)(30,206,162,118,74)(31,207,163,119,75)(32,208,164,120,76)(33,209,165,121,77)(34,210,166,122,78)(35,211,167,123,79)(36,212,168,124,80)(37,213,169,125,81)(38,214,170,126,82)(39,215,171,127,83)(40,216,172,128,84)(41,217,173,129,85)(42,218,174,130,86)(43,219,175,131,87)(44,220,176,132,88)(221,397,353,309,265)(222,398,354,310,266)(223,399,355,311,267)(224,400,356,312,268)(225,401,357,313,269)(226,402,358,314,270)(227,403,359,315,271)(228,404,360,316,272)(229,405,361,317,273)(230,406,362,318,274)(231,407,363,319,275)(232,408,364,320,276)(233,409,365,321,277)(234,410,366,322,278)(235,411,367,323,279)(236,412,368,324,280)(237,413,369,325,281)(238,414,370,326,282)(239,415,371,327,283)(240,416,372,328,284)(241,417,373,329,285)(242,418,374,330,286)(243,419,375,331,287)(244,420,376,332,288)(245,421,377,333,289)(246,422,378,334,290)(247,423,379,335,291)(248,424,380,336,292)(249,425,381,337,293)(250,426,382,338,294)(251,427,383,339,295)(252,428,384,340,296)(253,429,385,341,297)(254,430,386,342,298)(255,431,387,343,299)(256,432,388,344,300)(257,433,389,345,301)(258,434,390,346,302)(259,435,391,347,303)(260,436,392,348,304)(261,437,393,349,305)(262,438,394,350,306)(263,439,395,351,307)(264,440,396,352,308), (1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33)(34,35,36,37,38,39,40,41,42,43,44)(45,46,47,48,49,50,51,52,53,54,55)(56,57,58,59,60,61,62,63,64,65,66)(67,68,69,70,71,72,73,74,75,76,77)(78,79,80,81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96,97,98,99)(100,101,102,103,104,105,106,107,108,109,110)(111,112,113,114,115,116,117,118,119,120,121)(122,123,124,125,126,127,128,129,130,131,132)(133,134,135,136,137,138,139,140,141,142,143)(144,145,146,147,148,149,150,151,152,153,154)(155,156,157,158,159,160,161,162,163,164,165)(166,167,168,169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184,185,186,187)(188,189,190,191,192,193,194,195,196,197,198)(199,200,201,202,203,204,205,206,207,208,209)(210,211,212,213,214,215,216,217,218,219,220)(221,222,223,224,225,226,227,228,229,230,231)(232,233,234,235,236,237,238,239,240,241,242)(243,244,245,246,247,248,249,250,251,252,253)(254,255,256,257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272,273,274,275)(276,277,278,279,280,281,282,283,284,285,286)(287,288,289,290,291,292,293,294,295,296,297)(298,299,300,301,302,303,304,305,306,307,308)(309,310,311,312,313,314,315,316,317,318,319)(320,321,322,323,324,325,326,327,328,329,330)(331,332,333,334,335,336,337,338,339,340,341)(342,343,344,345,346,347,348,349,350,351,352)(353,354,355,356,357,358,359,360,361,362,363)(364,365,366,367,368,369,370,371,372,373,374)(375,376,377,378,379,380,381,382,383,384,385)(386,387,388,389,390,391,392,393,394,395,396)(397,398,399,400,401,402,403,404,405,406,407)(408,409,410,411,412,413,414,415,416,417,418)(419,420,421,422,423,424,425,426,427,428,429)(430,431,432,433,434,435,436,437,438,439,440), (1,263,34,241,12,252,23,230)(2,262,35,240,13,251,24,229)(3,261,36,239,14,250,25,228)(4,260,37,238,15,249,26,227)(5,259,38,237,16,248,27,226)(6,258,39,236,17,247,28,225)(7,257,40,235,18,246,29,224)(8,256,41,234,19,245,30,223)(9,255,42,233,20,244,31,222)(10,254,43,232,21,243,32,221)(11,264,44,242,22,253,33,231)(45,307,78,285,56,296,67,274)(46,306,79,284,57,295,68,273)(47,305,80,283,58,294,69,272)(48,304,81,282,59,293,70,271)(49,303,82,281,60,292,71,270)(50,302,83,280,61,291,72,269)(51,301,84,279,62,290,73,268)(52,300,85,278,63,289,74,267)(53,299,86,277,64,288,75,266)(54,298,87,276,65,287,76,265)(55,308,88,286,66,297,77,275)(89,351,122,329,100,340,111,318)(90,350,123,328,101,339,112,317)(91,349,124,327,102,338,113,316)(92,348,125,326,103,337,114,315)(93,347,126,325,104,336,115,314)(94,346,127,324,105,335,116,313)(95,345,128,323,106,334,117,312)(96,344,129,322,107,333,118,311)(97,343,130,321,108,332,119,310)(98,342,131,320,109,331,120,309)(99,352,132,330,110,341,121,319)(133,395,166,373,144,384,155,362)(134,394,167,372,145,383,156,361)(135,393,168,371,146,382,157,360)(136,392,169,370,147,381,158,359)(137,391,170,369,148,380,159,358)(138,390,171,368,149,379,160,357)(139,389,172,367,150,378,161,356)(140,388,173,366,151,377,162,355)(141,387,174,365,152,376,163,354)(142,386,175,364,153,375,164,353)(143,396,176,374,154,385,165,363)(177,439,210,417,188,428,199,406)(178,438,211,416,189,427,200,405)(179,437,212,415,190,426,201,404)(180,436,213,414,191,425,202,403)(181,435,214,413,192,424,203,402)(182,434,215,412,193,423,204,401)(183,433,216,411,194,422,205,400)(184,432,217,410,195,421,206,399)(185,431,218,409,196,420,207,398)(186,430,219,408,197,419,208,397)(187,440,220,418,198,429,209,407)>;
G:=Group( (1,177,133,89,45)(2,178,134,90,46)(3,179,135,91,47)(4,180,136,92,48)(5,181,137,93,49)(6,182,138,94,50)(7,183,139,95,51)(8,184,140,96,52)(9,185,141,97,53)(10,186,142,98,54)(11,187,143,99,55)(12,188,144,100,56)(13,189,145,101,57)(14,190,146,102,58)(15,191,147,103,59)(16,192,148,104,60)(17,193,149,105,61)(18,194,150,106,62)(19,195,151,107,63)(20,196,152,108,64)(21,197,153,109,65)(22,198,154,110,66)(23,199,155,111,67)(24,200,156,112,68)(25,201,157,113,69)(26,202,158,114,70)(27,203,159,115,71)(28,204,160,116,72)(29,205,161,117,73)(30,206,162,118,74)(31,207,163,119,75)(32,208,164,120,76)(33,209,165,121,77)(34,210,166,122,78)(35,211,167,123,79)(36,212,168,124,80)(37,213,169,125,81)(38,214,170,126,82)(39,215,171,127,83)(40,216,172,128,84)(41,217,173,129,85)(42,218,174,130,86)(43,219,175,131,87)(44,220,176,132,88)(221,397,353,309,265)(222,398,354,310,266)(223,399,355,311,267)(224,400,356,312,268)(225,401,357,313,269)(226,402,358,314,270)(227,403,359,315,271)(228,404,360,316,272)(229,405,361,317,273)(230,406,362,318,274)(231,407,363,319,275)(232,408,364,320,276)(233,409,365,321,277)(234,410,366,322,278)(235,411,367,323,279)(236,412,368,324,280)(237,413,369,325,281)(238,414,370,326,282)(239,415,371,327,283)(240,416,372,328,284)(241,417,373,329,285)(242,418,374,330,286)(243,419,375,331,287)(244,420,376,332,288)(245,421,377,333,289)(246,422,378,334,290)(247,423,379,335,291)(248,424,380,336,292)(249,425,381,337,293)(250,426,382,338,294)(251,427,383,339,295)(252,428,384,340,296)(253,429,385,341,297)(254,430,386,342,298)(255,431,387,343,299)(256,432,388,344,300)(257,433,389,345,301)(258,434,390,346,302)(259,435,391,347,303)(260,436,392,348,304)(261,437,393,349,305)(262,438,394,350,306)(263,439,395,351,307)(264,440,396,352,308), (1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33)(34,35,36,37,38,39,40,41,42,43,44)(45,46,47,48,49,50,51,52,53,54,55)(56,57,58,59,60,61,62,63,64,65,66)(67,68,69,70,71,72,73,74,75,76,77)(78,79,80,81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96,97,98,99)(100,101,102,103,104,105,106,107,108,109,110)(111,112,113,114,115,116,117,118,119,120,121)(122,123,124,125,126,127,128,129,130,131,132)(133,134,135,136,137,138,139,140,141,142,143)(144,145,146,147,148,149,150,151,152,153,154)(155,156,157,158,159,160,161,162,163,164,165)(166,167,168,169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184,185,186,187)(188,189,190,191,192,193,194,195,196,197,198)(199,200,201,202,203,204,205,206,207,208,209)(210,211,212,213,214,215,216,217,218,219,220)(221,222,223,224,225,226,227,228,229,230,231)(232,233,234,235,236,237,238,239,240,241,242)(243,244,245,246,247,248,249,250,251,252,253)(254,255,256,257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272,273,274,275)(276,277,278,279,280,281,282,283,284,285,286)(287,288,289,290,291,292,293,294,295,296,297)(298,299,300,301,302,303,304,305,306,307,308)(309,310,311,312,313,314,315,316,317,318,319)(320,321,322,323,324,325,326,327,328,329,330)(331,332,333,334,335,336,337,338,339,340,341)(342,343,344,345,346,347,348,349,350,351,352)(353,354,355,356,357,358,359,360,361,362,363)(364,365,366,367,368,369,370,371,372,373,374)(375,376,377,378,379,380,381,382,383,384,385)(386,387,388,389,390,391,392,393,394,395,396)(397,398,399,400,401,402,403,404,405,406,407)(408,409,410,411,412,413,414,415,416,417,418)(419,420,421,422,423,424,425,426,427,428,429)(430,431,432,433,434,435,436,437,438,439,440), (1,263,34,241,12,252,23,230)(2,262,35,240,13,251,24,229)(3,261,36,239,14,250,25,228)(4,260,37,238,15,249,26,227)(5,259,38,237,16,248,27,226)(6,258,39,236,17,247,28,225)(7,257,40,235,18,246,29,224)(8,256,41,234,19,245,30,223)(9,255,42,233,20,244,31,222)(10,254,43,232,21,243,32,221)(11,264,44,242,22,253,33,231)(45,307,78,285,56,296,67,274)(46,306,79,284,57,295,68,273)(47,305,80,283,58,294,69,272)(48,304,81,282,59,293,70,271)(49,303,82,281,60,292,71,270)(50,302,83,280,61,291,72,269)(51,301,84,279,62,290,73,268)(52,300,85,278,63,289,74,267)(53,299,86,277,64,288,75,266)(54,298,87,276,65,287,76,265)(55,308,88,286,66,297,77,275)(89,351,122,329,100,340,111,318)(90,350,123,328,101,339,112,317)(91,349,124,327,102,338,113,316)(92,348,125,326,103,337,114,315)(93,347,126,325,104,336,115,314)(94,346,127,324,105,335,116,313)(95,345,128,323,106,334,117,312)(96,344,129,322,107,333,118,311)(97,343,130,321,108,332,119,310)(98,342,131,320,109,331,120,309)(99,352,132,330,110,341,121,319)(133,395,166,373,144,384,155,362)(134,394,167,372,145,383,156,361)(135,393,168,371,146,382,157,360)(136,392,169,370,147,381,158,359)(137,391,170,369,148,380,159,358)(138,390,171,368,149,379,160,357)(139,389,172,367,150,378,161,356)(140,388,173,366,151,377,162,355)(141,387,174,365,152,376,163,354)(142,386,175,364,153,375,164,353)(143,396,176,374,154,385,165,363)(177,439,210,417,188,428,199,406)(178,438,211,416,189,427,200,405)(179,437,212,415,190,426,201,404)(180,436,213,414,191,425,202,403)(181,435,214,413,192,424,203,402)(182,434,215,412,193,423,204,401)(183,433,216,411,194,422,205,400)(184,432,217,410,195,421,206,399)(185,431,218,409,196,420,207,398)(186,430,219,408,197,419,208,397)(187,440,220,418,198,429,209,407) );
G=PermutationGroup([[(1,177,133,89,45),(2,178,134,90,46),(3,179,135,91,47),(4,180,136,92,48),(5,181,137,93,49),(6,182,138,94,50),(7,183,139,95,51),(8,184,140,96,52),(9,185,141,97,53),(10,186,142,98,54),(11,187,143,99,55),(12,188,144,100,56),(13,189,145,101,57),(14,190,146,102,58),(15,191,147,103,59),(16,192,148,104,60),(17,193,149,105,61),(18,194,150,106,62),(19,195,151,107,63),(20,196,152,108,64),(21,197,153,109,65),(22,198,154,110,66),(23,199,155,111,67),(24,200,156,112,68),(25,201,157,113,69),(26,202,158,114,70),(27,203,159,115,71),(28,204,160,116,72),(29,205,161,117,73),(30,206,162,118,74),(31,207,163,119,75),(32,208,164,120,76),(33,209,165,121,77),(34,210,166,122,78),(35,211,167,123,79),(36,212,168,124,80),(37,213,169,125,81),(38,214,170,126,82),(39,215,171,127,83),(40,216,172,128,84),(41,217,173,129,85),(42,218,174,130,86),(43,219,175,131,87),(44,220,176,132,88),(221,397,353,309,265),(222,398,354,310,266),(223,399,355,311,267),(224,400,356,312,268),(225,401,357,313,269),(226,402,358,314,270),(227,403,359,315,271),(228,404,360,316,272),(229,405,361,317,273),(230,406,362,318,274),(231,407,363,319,275),(232,408,364,320,276),(233,409,365,321,277),(234,410,366,322,278),(235,411,367,323,279),(236,412,368,324,280),(237,413,369,325,281),(238,414,370,326,282),(239,415,371,327,283),(240,416,372,328,284),(241,417,373,329,285),(242,418,374,330,286),(243,419,375,331,287),(244,420,376,332,288),(245,421,377,333,289),(246,422,378,334,290),(247,423,379,335,291),(248,424,380,336,292),(249,425,381,337,293),(250,426,382,338,294),(251,427,383,339,295),(252,428,384,340,296),(253,429,385,341,297),(254,430,386,342,298),(255,431,387,343,299),(256,432,388,344,300),(257,433,389,345,301),(258,434,390,346,302),(259,435,391,347,303),(260,436,392,348,304),(261,437,393,349,305),(262,438,394,350,306),(263,439,395,351,307),(264,440,396,352,308)], [(1,2,3,4,5,6,7,8,9,10,11),(12,13,14,15,16,17,18,19,20,21,22),(23,24,25,26,27,28,29,30,31,32,33),(34,35,36,37,38,39,40,41,42,43,44),(45,46,47,48,49,50,51,52,53,54,55),(56,57,58,59,60,61,62,63,64,65,66),(67,68,69,70,71,72,73,74,75,76,77),(78,79,80,81,82,83,84,85,86,87,88),(89,90,91,92,93,94,95,96,97,98,99),(100,101,102,103,104,105,106,107,108,109,110),(111,112,113,114,115,116,117,118,119,120,121),(122,123,124,125,126,127,128,129,130,131,132),(133,134,135,136,137,138,139,140,141,142,143),(144,145,146,147,148,149,150,151,152,153,154),(155,156,157,158,159,160,161,162,163,164,165),(166,167,168,169,170,171,172,173,174,175,176),(177,178,179,180,181,182,183,184,185,186,187),(188,189,190,191,192,193,194,195,196,197,198),(199,200,201,202,203,204,205,206,207,208,209),(210,211,212,213,214,215,216,217,218,219,220),(221,222,223,224,225,226,227,228,229,230,231),(232,233,234,235,236,237,238,239,240,241,242),(243,244,245,246,247,248,249,250,251,252,253),(254,255,256,257,258,259,260,261,262,263,264),(265,266,267,268,269,270,271,272,273,274,275),(276,277,278,279,280,281,282,283,284,285,286),(287,288,289,290,291,292,293,294,295,296,297),(298,299,300,301,302,303,304,305,306,307,308),(309,310,311,312,313,314,315,316,317,318,319),(320,321,322,323,324,325,326,327,328,329,330),(331,332,333,334,335,336,337,338,339,340,341),(342,343,344,345,346,347,348,349,350,351,352),(353,354,355,356,357,358,359,360,361,362,363),(364,365,366,367,368,369,370,371,372,373,374),(375,376,377,378,379,380,381,382,383,384,385),(386,387,388,389,390,391,392,393,394,395,396),(397,398,399,400,401,402,403,404,405,406,407),(408,409,410,411,412,413,414,415,416,417,418),(419,420,421,422,423,424,425,426,427,428,429),(430,431,432,433,434,435,436,437,438,439,440)], [(1,263,34,241,12,252,23,230),(2,262,35,240,13,251,24,229),(3,261,36,239,14,250,25,228),(4,260,37,238,15,249,26,227),(5,259,38,237,16,248,27,226),(6,258,39,236,17,247,28,225),(7,257,40,235,18,246,29,224),(8,256,41,234,19,245,30,223),(9,255,42,233,20,244,31,222),(10,254,43,232,21,243,32,221),(11,264,44,242,22,253,33,231),(45,307,78,285,56,296,67,274),(46,306,79,284,57,295,68,273),(47,305,80,283,58,294,69,272),(48,304,81,282,59,293,70,271),(49,303,82,281,60,292,71,270),(50,302,83,280,61,291,72,269),(51,301,84,279,62,290,73,268),(52,300,85,278,63,289,74,267),(53,299,86,277,64,288,75,266),(54,298,87,276,65,287,76,265),(55,308,88,286,66,297,77,275),(89,351,122,329,100,340,111,318),(90,350,123,328,101,339,112,317),(91,349,124,327,102,338,113,316),(92,348,125,326,103,337,114,315),(93,347,126,325,104,336,115,314),(94,346,127,324,105,335,116,313),(95,345,128,323,106,334,117,312),(96,344,129,322,107,333,118,311),(97,343,130,321,108,332,119,310),(98,342,131,320,109,331,120,309),(99,352,132,330,110,341,121,319),(133,395,166,373,144,384,155,362),(134,394,167,372,145,383,156,361),(135,393,168,371,146,382,157,360),(136,392,169,370,147,381,158,359),(137,391,170,369,148,380,159,358),(138,390,171,368,149,379,160,357),(139,389,172,367,150,378,161,356),(140,388,173,366,151,377,162,355),(141,387,174,365,152,376,163,354),(142,386,175,364,153,375,164,353),(143,396,176,374,154,385,165,363),(177,439,210,417,188,428,199,406),(178,438,211,416,189,427,200,405),(179,437,212,415,190,426,201,404),(180,436,213,414,191,425,202,403),(181,435,214,413,192,424,203,402),(182,434,215,412,193,423,204,401),(183,433,216,411,194,422,205,400),(184,432,217,410,195,421,206,399),(185,431,218,409,196,420,207,398),(186,430,219,408,197,419,208,397),(187,440,220,418,198,429,209,407)]])
140 conjugacy classes
| class | 1 | 2 | 4A | 4B | 5A | 5B | 5C | 5D | 8A | 8B | 8C | 8D | 10A | 10B | 10C | 10D | 11A | ··· | 11E | 20A | ··· | 20H | 22A | ··· | 22E | 40A | ··· | 40P | 44A | ··· | 44J | 55A | ··· | 55T | 110A | ··· | 110T | 220A | ··· | 220AN |
| order | 1 | 2 | 4 | 4 | 5 | 5 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 11 | ··· | 11 | 20 | ··· | 20 | 22 | ··· | 22 | 40 | ··· | 40 | 44 | ··· | 44 | 55 | ··· | 55 | 110 | ··· | 110 | 220 | ··· | 220 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 11 | 11 | 11 | 11 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 11 | ··· | 11 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
140 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||||||
| image | C1 | C2 | C4 | C5 | C8 | C10 | C20 | C40 | D11 | Dic11 | C11⋊C8 | C5×D11 | C5×Dic11 | C5×C11⋊C8 |
| kernel | C5×C11⋊C8 | C220 | C110 | C11⋊C8 | C55 | C44 | C22 | C11 | C20 | C10 | C5 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 4 | 4 | 8 | 16 | 5 | 5 | 10 | 20 | 20 | 40 |
Matrix representation of C5×C11⋊C8 ►in GL3(𝔽881) generated by
| 286 | 0 | 0 |
| 0 | 286 | 0 |
| 0 | 0 | 286 |
| 1 | 0 | 0 |
| 0 | 680 | 880 |
| 0 | 681 | 880 |
| 662 | 0 | 0 |
| 0 | 635 | 383 |
| 0 | 792 | 246 |
G:=sub<GL(3,GF(881))| [286,0,0,0,286,0,0,0,286],[1,0,0,0,680,681,0,880,880],[662,0,0,0,635,792,0,383,246] >;
C5×C11⋊C8 in GAP, Magma, Sage, TeX
C_5\times C_{11}\rtimes C_8 % in TeX
G:=Group("C5xC11:C8"); // GroupNames label
G:=SmallGroup(440,4);
// by ID
G=gap.SmallGroup(440,4);
# by ID
G:=PCGroup([5,-2,-5,-2,-2,-11,50,42,10004]);
// Polycyclic
G:=Group<a,b,c|a^5=b^11=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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